Abstract

A new instrument for rapid and accurate measurement of the Mueller matrix is described. Distinct measurements of all sixteen elements are made simultaneously and with an absolute accuracy of 1–5%. The instrument employs electrooptic modulators. Results are presented for several simple optical devices and systems.

© 1980 Optical Society of America

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References

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  1. F. Perrin, J. Chem. Phys. 10, 414 (1942).
    [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. J. W. Simmons, M. J. Guttmann, States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass., 1970).
  4. G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
    [CrossRef]
  5. S. J. Hitzfelder, G. N. Plass, G. W. Kattawar, Appl. Opt. 15, 2489 (1976).
    [CrossRef] [PubMed]
  6. G. W. Kattawar, G. N. Plass, Appl. Opt. 15, 3166 (1976).
    [CrossRef] [PubMed]
  7. G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
    [CrossRef]
  8. Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).
  9. Ye. A. Kadyshevich, Yu. S. Lyubovtseva, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 659 (1973).
  10. Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).
  11. G. Mie, Ann. Phys. 25, 377 (1908).
    [CrossRef]
  12. Lord Rayleigh, Philos. Mag. 36, 365 (1918).
  13. J. R. Wait, Can. J. Phys. 33, 189 (1955).
    [CrossRef]
  14. S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975).
    [PubMed]
  15. E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
    [CrossRef]
  16. G. W. Kattawar, T. J. Humphreys, Appl. Opt. in press.
  17. C. Yeh, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).
  18. B. S. Pritchard, W. G. Elliott, J. Opt. Soc. Am. 50, 191 (1960).
    [CrossRef]
  19. G. V. Rozenberg, Adv. Phys. Sci. USSR 11, 353 (1968).
  20. G. I. Gorchakov, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 3, (1967).
  21. A. C. Holland, G. Gagne, Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  22. G. F. Beardsley, J. Opt. Soc. Am. 58, 52 (1968).Complete references to this work can be found in Ref. 10.
    [CrossRef]
  23. J. C. Kemp, J. Opt. Soc. Am. 59, 950 (1969).
  24. L. F. Mollenauer, D. Downie, H. Engstrom, W. B. Grant, Appl. Opt. 8, 661 (1969).
    [CrossRef] [PubMed]
  25. J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
    [CrossRef]
  26. J. Tinbergen, Astron. Astrophys. 23, 25 (1973).
  27. G. R. Boyer, B. F. Lamouroux, B. S. Prade, Appl. Opt. 18, 1217 (1979).
    [CrossRef] [PubMed]
  28. D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
    [CrossRef] [PubMed]
  29. C. Cortese, F. Aramu, V. Maxia, Opt. Commun. 2, 296 (1975).
    [CrossRef]
  30. P. S. Hauge, Proc. Soc. Photo-Opt. Instrum. Eng. 88, 3 (1976).
  31. A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
    [CrossRef]
  32. R. C. Thompson, E. S. Fry, J. Opt. Soc. Am. 64, 1399A (1974).
  33. R. J. Perry, A. J. Hunt, D. R. Huffman, Appl. Opt. 17, 2700 (1978).
    [CrossRef] [PubMed]
  34. W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
    [CrossRef] [PubMed]
  35. R. M. A. Azzam, Opt. Lett. 2, 148 (1978).
    [CrossRef] [PubMed]
  36. R. C. Thompson, J. Opt. Soc. Am. 66, 1134 (1976).
  37. R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).
  38. R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M U. (1978).
  39. R. Goldstein, “Pockels Cell Primer,” Laser Focus, p. 21 (Feb.1968).
  40. B. H. Billings, J. Opt. Soc. Am. 39, 802 (1949).
    [CrossRef]
  41. R. C. Thompson, J. R. Bottiger, E. S. Fry, Proc. Soc. Photo-Opt. Instrum. Eng. 160, 43 (1978).
  42. J. R. Bottiger, E. S. Fry, R. C. Thompson, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

1979 (1)

1978 (3)

1977 (1)

R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).

1976 (6)

R. C. Thompson, J. Opt. Soc. Am. 66, 1134 (1976).

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

P. S. Hauge, Proc. Soc. Photo-Opt. Instrum. Eng. 88, 3 (1976).

S. J. Hitzfelder, G. N. Plass, G. W. Kattawar, Appl. Opt. 15, 2489 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, Appl. Opt. 15, 3166 (1976).
[CrossRef] [PubMed]

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

1975 (3)

1974 (1)

R. C. Thompson, E. S. Fry, J. Opt. Soc. Am. 64, 1399A (1974).

1973 (5)

J. Tinbergen, Astron. Astrophys. 23, 25 (1973).

A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
[CrossRef]

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 659 (1973).

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

1972 (1)

J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
[CrossRef]

1971 (2)

G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
[CrossRef]

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).

1970 (1)

1969 (2)

1968 (3)

R. Goldstein, “Pockels Cell Primer,” Laser Focus, p. 21 (Feb.1968).

G. F. Beardsley, J. Opt. Soc. Am. 58, 52 (1968).Complete references to this work can be found in Ref. 10.
[CrossRef]

G. V. Rozenberg, Adv. Phys. Sci. USSR 11, 353 (1968).

1967 (1)

G. I. Gorchakov, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 3, (1967).

1960 (1)

1955 (1)

J. R. Wait, Can. J. Phys. 33, 189 (1955).
[CrossRef]

1949 (1)

1942 (1)

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

1918 (1)

Lord Rayleigh, Philos. Mag. 36, 365 (1918).

1908 (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Adams, C. N.

G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
[CrossRef]

Aramu, F.

C. Cortese, F. Aramu, V. Maxia, Opt. Commun. 2, 296 (1975).
[CrossRef]

Asano, S.

Aspnes, D. E.

Azzam, R. M. A.

Beardsley, G. F.

Bickel, W. S.

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Billings, B. H.

Bottiger, J. R.

R. C. Thompson, J. R. Bottiger, E. S. Fry, Proc. Soc. Photo-Opt. Instrum. Eng. 160, 43 (1978).

R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Boyer, G. R.

Cortese, C.

C. Cortese, F. Aramu, V. Maxia, Opt. Commun. 2, 296 (1975).
[CrossRef]

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Downie, D.

Elliott, W. G.

Engstrom, H.

Fry, E. S.

R. C. Thompson, J. R. Bottiger, E. S. Fry, Proc. Soc. Photo-Opt. Instrum. Eng. 160, 43 (1978).

R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).

R. C. Thompson, E. S. Fry, J. Opt. Soc. Am. 64, 1399A (1974).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Gagne, G.

Goldstein, R.

R. Goldstein, “Pockels Cell Primer,” Laser Focus, p. 21 (Feb.1968).

Gorchakov, G. I.

G. I. Gorchakov, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 3, (1967).

Grant, W. B.

Guinn, J. A.

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

Guttmann, M. J.

J. W. Simmons, M. J. Guttmann, States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass., 1970).

Hauge, P. S.

P. S. Hauge, Proc. Soc. Photo-Opt. Instrum. Eng. 88, 3 (1976).

Hitzfelder, S. J.

Holland, A. C.

Huffman, D. R.

Huffman, D.R.

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Humphreys, T. J.

G. W. Kattawar, T. J. Humphreys, Appl. Opt. in press.

Hunt, A. J.

Kadyshevich, Ye. A.

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 659 (1973).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).

Kattawar, G. W.

S. J. Hitzfelder, G. N. Plass, G. W. Kattawar, Appl. Opt. 15, 2489 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, Appl. Opt. 15, 3166 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
[CrossRef]

G. W. Kattawar, T. J. Humphreys, Appl. Opt. in press.

Kemp, J. C.

J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
[CrossRef]

J. C. Kemp, J. Opt. Soc. Am. 59, 950 (1969).

Kilkson, R.

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Lamouroux, B. F.

Lyubovtseva, Yu. S.

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 659 (1973).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).

Maxia, V.

C. Cortese, F. Aramu, V. Maxia, Opt. Commun. 2, 296 (1975).
[CrossRef]

Mie, G.

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Mollenauer, L. F.

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

Perry, R. J.

Plakhina, I. N.

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).

Plass, G. N.

S. J. Hitzfelder, G. N. Plass, G. W. Kattawar, Appl. Opt. 15, 2489 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, Appl. Opt. 15, 3166 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
[CrossRef]

Prade, B. S.

Pritchard, B. S.

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, Philos. Mag. 36, 365 (1918).

Rozenberg, G. V.

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

G. V. Rozenberg, Adv. Phys. Sci. USSR 11, 353 (1968).

G. I. Gorchakov, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 3, (1967).

Simmons, J. W.

J. W. Simmons, M. J. Guttmann, States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass., 1970).

Studna, A. A.

Swedlund, J. B.

J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
[CrossRef]

Thompson, R. C.

R. C. Thompson, J. R. Bottiger, E. S. Fry, Proc. Soc. Photo-Opt. Instrum. Eng. 160, 43 (1978).

R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).

R. C. Thompson, J. Opt. Soc. Am. 66, 1134 (1976).

R. C. Thompson, E. S. Fry, J. Opt. Soc. Am. 64, 1399A (1974).

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M U. (1978).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Tinbergen, J.

J. Tinbergen, Astron. Astrophys. 23, 25 (1973).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wait, J. R.

J. R. Wait, Can. J. Phys. 33, 189 (1955).
[CrossRef]

Wolstencroft, R. D.

J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
[CrossRef]

Yamamoto, G.

Yeh, C.

C. Yeh, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Adv. Phys. Sci. USSR (1)

G. V. Rozenberg, Adv. Phys. Sci. USSR 11, 353 (1968).

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Appl. Opt. (8)

Astron. Astrophys. (1)

J. Tinbergen, Astron. Astrophys. 23, 25 (1973).

Astrophys. J. (3)

J. C. Kemp, R. D. Wolstencroft, J. B. Swedlund, Astrophys. J. 177, 177 (1972).
[CrossRef]

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[CrossRef]

G. W. Kattawar, G. N. Plass, C. N. Adams, Astrophys. J. 170, 371 (1971).
[CrossRef]

Can. J. Phys. (1)

J. R. Wait, Can. J. Phys. 33, 189 (1955).
[CrossRef]

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (4)

G. I. Gorchakov, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 3, (1967).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, I. N. Plakhina, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 7, 367 (1971).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 659 (1973).

Ye. A. Kadyshevich, Yu. S. Lyubovtseva, G. V. Rozenberg, Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 12, 106 (1976).

J. Chem. Phys. (1)

F. Perrin, J. Chem. Phys. 10, 414 (1942).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Phys. Oceanogr. (1)

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Oceanogr. 3, 353 (1973).
[CrossRef]

Laser Focus (1)

R. Goldstein, “Pockels Cell Primer,” Laser Focus, p. 21 (Feb.1968).

Opt. Commun. (1)

C. Cortese, F. Aramu, V. Maxia, Opt. Commun. 2, 296 (1975).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (1)

Lord Rayleigh, Philos. Mag. 36, 365 (1918).

Proc. Natl. Acad. Sci. USA (1)

W. S. Bickel, J. F. Davidson, D.R. Huffman, R. Kilkson, Proc. Natl. Acad. Sci. USA 73, 486 (1976).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

R. C. Thompson, E. S. Fry, J. R. Bottiger, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 152 (1977).

P. S. Hauge, Proc. Soc. Photo-Opt. Instrum. Eng. 88, 3 (1976).

R. C. Thompson, J. R. Bottiger, E. S. Fry, Proc. Soc. Photo-Opt. Instrum. Eng. 160, 43 (1978).

Rev. Sci. Instrum. (1)

A. J. Hunt, D. R. Huffman, Rev. Sci. Instrum. 44, 1753 (1973).
[CrossRef]

Other (6)

R. C. Thompson, “An Electro-Optic Light Scattering Photometric Polarimeter,” Ph.D. Thesis, Texas A&M U. (1978).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

J. W. Simmons, M. J. Guttmann, States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass., 1970).

G. W. Kattawar, T. J. Humphreys, Appl. Opt. in press.

C. Yeh, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

J. R. Bottiger, E. S. Fry, R. C. Thompson, in Proceedings, International Workshop on Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the instrument. The angle θ is the scattering angle. The orientations of the transmission axes and fast axes of the polarizers and retarders, respectively, are given by γ.

Fig. 2
Fig. 2

Linear combinations of primary frequencies at which each matrix element appears in first order in the output intensity. The numerical value of the frequency at which we observe each matrix element is also given.

Fig. 3
Fig. 3

Schematic of the electronics.

Fig. 4
Fig. 4

Flow chart for generation of the various reference frequencies. Analog multipliers are used to produce the sum and difference frequencies.

Fig. 5
Fig. 5

Circuit for generating a reference frequency. Standard operational amplifiers and analog multipliers are used. Capacitor, resistor, and inductor values depend on the particular reference frequency.

Fig. 6
Fig. 6

Circuit for phase sensitive detector (PSD). Standard operational amplifiers and analog multipliers are used.

Fig. 7
Fig. 7

First-order terms that arise due to misalignment of the optical system. They are presented in the positions corresponding to the reference frequencies at which they appear.

Fig. 8
Fig. 8

Measured matrix of a linear polarizer. The abscissa is the angle between the transmission axis and the reference plane.

Fig. 9
Fig. 9

Measured matrix of a linear retarder at 442 nm. This was nominally a quarterwave retarder at 633 nm.

Fig. 10
Fig. 10

Measured matrix of an aqueous suspension of 91.0-nm diam polystyrene spheres. The wavelength is 633 nm. This is a very Rayleigh-like system, and the data are nearly indistinguishable from Mie calculations.

Fig. 11
Fig. 11

Measured matrix for a single polystyrene sphere suspended in air in an inhomogeneous electric field. The dotted curves are Mie calculations using a diameter of 1.110 μm and an index of refraction of 1.6144.

Tables (1)

Tables Icon

Table I Values of Jn (δ0); δ0 = 2.404 rad

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

S = { I Q U V } .
S e = SS i ,
A = A n x . . . A 3 × A 2 × A 1 .
F ( θ ) = F ( θ ) / f 11 ( θ ) .
1 f i j ( θ ) + 1 ,
P j = 1 2 { 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 } .
M 1 ( 4 ) = { 1 0 0 0 0 cos δ 1 ( 4 ) 0 sin δ 1 ( 4 ) 0 0 1 0 0 sin δ 1 ( 4 ) 0 cos δ 1 ( 4 ) } .
M 2 ( 3 ) = { 1 0 0 0 0 1 0 0 0 0 cos δ 2 ( 3 ) sin δ 2 ( 3 ) 0 0 sin δ 2 ( 3 ) cos δ 2 ( 3 ) } .
F = { f 11 f 12 f 13 f 14 f 21 f 22 f 23 f 24 f 31 f 32 f 33 f 34 f 41 f 42 f 43 f 44 } .
S 0 = I 0 { 1 1 0 0 } ,
S f = I f { 1 1 0 0 } ,
S f I 0 ( P 2 M 4 M 3 FM 2 M 1 ) S 0 .
I f = I 0 2 ( f 11 + f 12 cos δ 1 + f 13 sin δ 1 sin δ 2 f 14 sin δ 1 cos δ 2 + f 21 cos δ 4 + f 22 cos δ 1 cos δ 4 + f 23 sin δ 1 sin δ 2 cos δ 4 f 24 sin δ 1 cos δ 2 cos δ 4 + f 31 sin δ 3 sin δ 4 + f 32 cos δ 1 sin δ 3 sin δ 4 + f 33 sin δ 1 sin δ 2 sin δ 3 sin δ 4 f 34 sin δ 1 cos δ 2 sin δ 3 sin δ 4 + f 41 cos δ 3 sin δ 4 + f 42 cos δ 1 cos δ 3 sin δ 4 + f 43 sin δ 1 sin δ 2 cos δ 3 sin δ 4 f 44 sin δ 1 cos δ 2 cos δ 3 sin δ 4 ) .
δ i = δ 0 i cos ω i t .
cos δ i = J 0 ( δ 0 i ) 2 J 2 ( δ 0 i ) cos 2 ω i t + 2 J 4 ( δ 0 i ) cos 4 ω i t . . . .
sin δ i = 2 J 1 ( δ 0 i ) cos ω i t 2 J 3 ( δ 0 i ) cos 3 ω i t + . . . .
k ω 1 ± l ω 2 ± m ω 3 ± n ω 4 , k , l , m , n = 0 , 1 , 2 , 3 , . . . .
sin δ 1 cos δ 2 = 2 J 1 ( δ 01 ) J 0 ( δ 02 ) cos ω 1 t 2 J 3 ( δ 01 ) J 0 ( δ 02 ) cos 3 ω 1 t 2 J 1 ( δ 01 ) J 2 ( δ 02 ) × { cos ( ω 1 + 2 ω 2 ) t + cos ( ω 1 2 ω 2 ) t } + 2 J 3 ( δ 01 ) J 2 ( δ 02 ) × { cos ( 3 ω 1 + 2 ω 2 ) t + cos ( 3 ω 1 2 ω 2 ) t } + . . . .
J 0 ( δ 0 i ) = 0 ,
δ 0 i ~ 2.404 rad .
ν 1 = 41.0 kHz , ν 3 = 1.0 kHz , ν 2 = 0.3 kHz , ν 4 = 1.00 kHz .
coeff f 32 coeff f 31 = 2 J 2 ( δ 01 ) J 3 ( δ 03 ) J 7 ( δ 04 ) 2 J 1 ( δ 03 ) J 1 ( δ 04 ) 1.9 × 10 4 ,
δ i = δ c i + δ 0 i cos ω i t ,
M ret = { 1 0 0 0 0 cos 2 2 γ + sin 2 2 γ cos δ ½ sin 4 γ ( 1 cos δ ) sin 2 γ sin δ 0 ½ sin 4 γ ( 1 cos δ ) sin 2 2 γ + cos 2 2 γ cos δ cos 2 γ sin δ 0 sin 2 γ sin δ cos 2 γ sin δ cos δ } .
sin ( δ c i ) , i = 1 , 2 , 3 , 4 J 0 ( δ 0 i ) , i = 1 , 2 , 3 , 4 cos ( 2 γ i ) , i = 1 , 4 sin ( 2 γ i ) , i = 2 , 3 } .
cos ( δ c i ) = 1 , i = 1 , 2 , 3 , 4 sin ( 2 γ i ) = 1 , i = 1 , 4 cos ( 2 γ i ) = 1 , i = 2 , 3 .
F Pol = { 1 cos 2 ψ sin 2 ψ 0 cos 2 ψ cos 2 2 ψ ½ sin 4 ψ 0 sin 2 ψ ½ sin 4 ψ sin 2 2 ψ 0 0 0 0 0 } .

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